Energy efficiency is one of the most critical issues in the design of wireless sensor networks. Observing that many sensor applications for object tracking can tolerate a certain degree of imprecision in location data of tracked objects, this paper studies precision-constrained approximate queries that trade answer precision for energy efficiency. We develop an Energy-conserving Approximate StoragE (EASE) scheme to efficiently answer approximate location queries by keeping error-bounded imprecise location data at some designated storage node. The data impreciseness is captured by a system parameter, i.e., approximation radius. We analyze the performance of EASE in terms of message complexity and derive the optimal setting of approximation radius. We show via extensive simulation experiments that, as compared to a conventional approach, the EASE scheme cuts down the network traffic by up to 96% and, in most cases, prolongs the network lifetime by a factor of 2-5.